In general, adaptive feedback cancellation schemes do not work well for tonal input signals.
In feedback cancellation systems in hearing aids, it is desirable that the output signal (i.e. receiver signal) u(n) is uncorrelated with the target input signal x(n), see FIG. 1. In this case, the algorithm used for updating the parameters of the feedback cancellation filter is typically operating under the theoretical conditions for which it is derived, and the performance of the feedback cancellation system can be good. However, unfortunately in hearing aid applications the output and input signals are typically not uncorrelated, since the output signal is in fact a delayed (and processed) version of the input signal; consequently, autocorrelation in the input signal leads to correlation between the output signal and the input signal. If correlation exists between these two signals, the adaptive algorithm (e.g., NLMS, RLS, see FIG. 1) will deliver a biased estimate of acoustic feedback. As a consequence, the feedback cancellation filter may not reduce the effect of feedback, but may in fact remove components of the target input signal, leading to signal distortions, potential loss in intelligibility (in the case that the input signal is speech) and sound quality (in the case of audio input signals), and resulting in a potentially unstable system leading to a howl.
The correlation problem mainly occurs for input signals x(n) containing signal components which are localized in the frequency domain, i.e., tone-like signal components. One way to reduce the impact of the tonal components on the estimate of the feedback cancellation filter is to filter them out of the signals e(n) and u(n) before the signals are presented to the adaptive algorithm. Such filtering is e.g. discussed in U.S. Pat. No. 6,831,986 B2, where an approach for removing the tonal components of e(n) and u(n) using a cascade of independent notch filters, each allowing removal of a single tonal component is proposed.